Review on the operator/Feynman diagram/dessins d’enfants

Abstract

In this paper, a short review of the operator/Feynman diagram/dessin d’enfants correspondence in the rank 3 tensor model is presented, and the cut and join operation is given in the language of dessin d’enfants as a straightforward development. We classify operators of the rank 3 tensor model up to level 5 with dessin d’enfants. (Based on the talk given by R. Y. at the international workshop “Randomness, Integrability and Representation Theory in Quantum Field Theory” at the Osaka City University Media Center on March 25, 2021.)